For independent events $A_1, A_2, \dots, A_n$,$P(A_i) = \frac{1}{i + 1}$ for $i = 1, 2, \dots, n$. Then the probability that none of the events will occur is:

Let $S_n = \sum_{k=1}^n k$ denote the sum of the first $n$ positive integers. The numbers $S_1, S_2, S_3, \ldots, S_{99}$ are written on $99$ cards. The probability of drawing a card with an even number written on it is

$A$ coin is tossed $3$ times. The probability of getting exactly two heads is

The events $A$ and $B$ have probabilities $0.25$ and $0.50$, respectively. The probability that both $A$ and $B$ occur simultaneously is $0.14$. Then, the probability that neither $A$ nor $B$ occurs is:

If $A$ and $B$ are events such that $P(A \cup B) = \frac{3}{4}$,$P(A \cap B) = \frac{1}{4}$,and $P(\overline{A}) = \frac{2}{3}$,then what is the value of $P(\overline{A} \cap B)$?

$A$ problem in mathematics is given to $4$ students whose chances of solving it individually are $\frac{1}{2}, \frac{1}{3}, \frac{1}{4},$ and $\frac{1}{5}.$ The probability that the problem will be solved by at least one student is